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Needs:
Real Convex Cones
Real Matrix Space
Real Positive Semidefinite Matrices
Needed by:
Real Positive Semidefinite Matrix Order
Real Spectrahedra
Links:
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Real Positive Semidefinite Matrix Cone

Why

The set of positive semidefinite matrices turns out to be a cone in the vector space of $n \times n$ matrices.

Main result

$\mathbfsf{S} _+^d$ is a convex, pointed, closed cone with interior $\mathbfsf{S} _{++}^d$ relative to $\mathbfsf{S} ^d$.1

The cone of positive definite matrices is open.


  1. Future editions will contain a proof. ↩︎
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